## ... not just a collection of units

The systematic structure of metric has a number of features.

### Basic units and prefixes

Metric is based on the principle that all measurable phenomena covered by the system - pretty well everything in the known natural world! - have one basic *named* unit. All the multiples and subdivisions then follow the same logical structure using *prefixes*. For example, the basic unit of power is the watt (named after a Briton). One thousand watts is a *kilo*watt, one million watts is a *mega*watt.

The basic named unit of length is the metre. Then for smaller distances, 1 metre = 1 000 *milli*metre, whereas for longer distances 1 000 metres = 1 *kilo*metre.

In exactly the same way, the basic named unit of mass or weight is the gram where we have 1 gram = 1 000 *milli*gram and 1 000 grams = 1 *kilo*gram.

### Logical symbols

The abbreviations also follow a simple logical pattern. The symbol 'm' for metre is used as the basis for mm to mean millimetre and km to represent kilometre.

Likewise where 'g' is used to mean gram we have mg for milligram and kg for kilogram.

There are many other prefixes for various multiples and subdivisions. They are all simple multiples of or divisions by ten and they all apply to every basic named unit.

### Links between related measurements

In everyday use, we need simple connections between measures of length, area, volume and mass.

Commonly used units of area are defined in terms of decimal multiples of square metres. In this case, ten times ten (ten squared):

Unit of area | Size |
---|---|

are (pronounced air) | 100 m^{2} |

hectare | 100 are |

km^{2} |
100 hectare |

In the opposite direction 1 m = 100 cm, therefore 1 m^{2} = 100 cm x 100 cm = 10 000 cm^{2}.

As for all metric measures, all we need to do is move the decimal point. In this case, we have moved it twice to multiply by 100:

100.000 becomes 10 000.0

In the case of volume we use the factor ten times ten times ten (ten cubed).

Unit of volume | Size |
---|---|

1 litre | 1 000 cm^{3} |

1 m^{3} |
1 000 litres |

Volume and mass are linked in a natural way by the properties of pure water. The gram was originally defined as the mass of 1 cubic centimetre of liquid water at a certain temperature. (The very small variation with temperature can be ignored for everyday purposes.)

Unit of volume | Mass of liquid water |
---|---|

cm^{3} |
gram |

litre | kilogram |

m^{3} |
tonne |

## Compare this system with imperial!

Unit | Size |
---|---|

square foot | 144 square inches (12 x 12) |

square yard | 9 square feet (3 x 3) |

acre | 4840 square yards (non-square unit of area defined by a strip 220 yards long by 22 yards wide, also 1 furlong long by 1 chain wide) |

square mile | 3 097 600 square yards (1760 x 1760) also 640 acre |

Unit | Size |
---|---|

UK fluid ounce |
1.734 cubic inches approximately |

UK pint | 20 fluid ounces or approximately 34.7 cubic inches |

gallon | 8 pints |

cubic foot | 1728 (12 x 12 x 12) cubic inches or approximately 6.2 gallons |

cubic yard | 27 cubic feet (3 x 3 x 3) |

Unit | Approximate mass of water |
---|---|

fluid ounce | ounce |

UK pint | 20 ounces = 1.25 pound |

UK gallon | 10 pounds |

cubic foot | 62 pound |

There is no hope of a single system to unite these measures. All the units have evolved independently for unrelated purposes. They may be quaint, but like much that is quaint, they belong in a museum.

## Power and energy

This is where the metric system really comes into its own. The units of energy and power are joules (J) and watts (W) respectively, regardless of whether you are measuring electrical, mechanical or chemical systems. The table below compares the single metric unit (the watt) with the diverse imperial units. (It should be noted that electrical units have always been metric.)

Application | Metric | Imperial |
---|---|---|

Motor car engine (mechanical) | kW | horse power |

Central heating boiler (chemical) | kW | BTU/h |

Light bulbs (electrical) | W | none defined |